A149483 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, 0, 1), (-1, 1, 0), (1, -1, 1), (1, 0, 1), (1, 1, -1)}.

1, 1, 4, 13, 58, 231, 1083, 4719, 22652, 103146, 501823, 2346298, 11508135, 54722503, 269804391, 1297724477, 6420746958, 31134239547, 154419290003, 753235565962, 3742452711191, 18336829105522, 91224524169927, 448509319572824, 2233479072961931, 11010623240374934, 54871480488519669, 271087435138530413

Offset

0,3

Links

Table of n, a(n) for n=0..27.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

Mathematica

aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A039626 A149481 A149482 * A149484 A149485 A006798

Adjacent sequences: A149480 A149481 A149482 * A149484 A149485 A149486

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved